A257722 Hexagonal numbers (A000384) that are the sum of eleven consecutive hexagonal numbers.

946, 1540, 13695, 1151403, 18773128, 1590903028, 25941294753, 2198372138061, 20904988593016, 35846699817610, 340877159895525, 28887334308843153, 471037447946228878, 39917653136343078778, 650898046192856866503, 55159780922590010984691

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..767

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,25091193602,-25091193602,0,0,0,0,0,0,-1,1).

Formula

G.f.: -11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)).

Example

946 is in the sequence because H(22) = 946 = 1 + 6 + 15 + 28 + 45 + 66 + 91 + 120 + 153 + 190 + 231 = H(1)+...+H(11).

Prog

(PARI) Vec(-11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)) + O(x^100))

Crossrefs

Cf. A257721, A257723, A257724.

Sequence in context: A322252 A351806 A119240 * A093247 A248785 A199924

Adjacent sequences: A257719 A257720 A257721 * A257723 A257724 A257725

Keyword

nonn,easy

Author

Colin Barker, May 06 2015

Status

approved